Tag Archives: math
A drunk man will find his way home, but a drunk bird may get lost forever
This elegant quote, which captures the essence of the mathematical fact that a 2-dimensional random walk is recurrent while in higher dimensions it is not, is attributed to Shizuo Kakutani. However, the original proof is due to George Pólya [1]. A -dimensional lattice is defined as a graph whose vertices are all points in with […]
Rayleigh’s monotonicity principle and AM-GM-HM inequalities
Rayleigh’s monotonicity principle states that if the resistances of a circuit of resistors are increased, the effective resistance between any two points can only increase. If they are decreased, they can only decrease. You can find a short proof in the Doyle-Snell book right here. One can use this intuitive principle to prove classic and […]
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